#ifndef GE_H
#define GE_H

#include "fe.h"

/*
ge means group element.

Here the group is the set of pairs (x,y) of field elements (see fe.h)
satisfying -x^2 + y^2 = 1 + d x^2y^2
where d = -121665/121666.

Representations:
  ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z
  ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT
  ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T
  ge_precomp (Duif): (y+x,y-x,2dxy)
*/

typedef struct {
  fe X;
  fe Y;
  fe Z;
} ge_p2;

typedef struct {
  fe X;
  fe Y;
  fe Z;
  fe T;
} ge_p3;

typedef struct {
  fe X;
  fe Y;
  fe Z;
  fe T;
} ge_p1p1;

typedef struct {
  fe yplusx;
  fe yminusx;
  fe xy2d;
} ge_precomp;

typedef struct {
  fe YplusX;
  fe YminusX;
  fe Z;
  fe T2d;
} ge_cached;

void
ge_p3_tobytes(unsigned char* s, const ge_p3* h);
void
ge_tobytes(unsigned char* s, const ge_p2* h);
int
ge_frombytes_negate_vartime(ge_p3* h, const unsigned char* s);

void
ge_add(ge_p1p1* r, const ge_p3* p, const ge_cached* q);
void
ge_sub(ge_p1p1* r, const ge_p3* p, const ge_cached* q);
void
ge_double_scalarmult_vartime(
    ge_p2* r, const unsigned char* a, const ge_p3* A, const unsigned char* b);
void
ge_madd(ge_p1p1* r, const ge_p3* p, const ge_precomp* q);
void
ge_msub(ge_p1p1* r, const ge_p3* p, const ge_precomp* q);
void
ge_scalarmult_base(ge_p3* h, const unsigned char* a);

void
ge_p1p1_to_p2(ge_p2* r, const ge_p1p1* p);
void
ge_p1p1_to_p3(ge_p3* r, const ge_p1p1* p);
void
ge_p2_0(ge_p2* h);
void
ge_p2_dbl(ge_p1p1* r, const ge_p2* p);
void
ge_p3_0(ge_p3* h);
void
ge_p3_dbl(ge_p1p1* r, const ge_p3* p);
void
ge_p3_to_cached(ge_cached* r, const ge_p3* p);
void
ge_p3_to_p2(ge_p2* r, const ge_p3* p);

#endif
